Professor Brennan's significant contributions to physics in Australia include:-
* His early work at Sydney University on cosmic ray showers;
* His work at Princeton in nuclear physics and plasma physics;
* His pioneering efforts in Sydney University in 1961-64 on the experimental elucidation of the behaviour of magnetohydrodynamic shock waves;
* His leading efforts in Flinders University in the propagation of electromagnetic waves in laboratory plasmas;
* His research since 1981 on wave propagation in a toroidal geometry at Sydney University.
In addition he has made significant contribution to physics in Australia through his membership and chairmanship of a number of national and international organisations including, Chairman of the ARGC and the National Research Fellowships Committee, Chairman of the AAEC, and Chairman of the International Fusion Research Council.